Entropy of a generic null surface from its associated Virasoro algebra

TL;DR

This paper generalizes the derivation of the entropy-area law for null surfaces by showing that a Virasoro algebra with a central charge exists for a broad class of null surfaces, leading to an entropy density of 1/4 per unit area.

Contribution

It extends the Virasoro algebra approach to compute entropy from black hole horizons to all null surfaces, establishing a universal entropy density.

Findings

Null surfaces possess a Virasoro algebra with a central charge.

The entropy density for null surfaces is universally 1/4 per unit area.

Previous horizon entropy results are special cases of this general property.

Abstract

Null surfaces act as one-way membranes, blocking information from those observers who do not cross them (e.g., in the black hole and the Rindler spacetimes) and these observers associate an entropy (and temperature) with the null surface. The black hole entropy can be computed from the central charge of an appropriately defined, local, Virasoro algebra on the horizon. We show that one can extend these ideas to a general class of null surfaces, all of which possess a Virasoro algebra and a central charge, leading to an entropy density (i.e., per unit area) which is just $(1/4)$. All the previously known results of associating entropy with horizons arise as special cases of this very general property of null surfaces demonstrated here and we believe this work represents the derivation of the entropy-area law in the most general context. The implications are discussed.